Wavelet transforms on vector spaces as a method of multispectral image characterisation

A new form of wavelet-based feature extraction has been developed for the multiresolution analysis of multispectral imagery, in which the wavelet components have vector amplitudes which can be used to characterise multispectral phenomena such as colour, in addition to scalar brightness. A vector-based approach enables the detection of unusual events which do not stand out in any of the individual scalar image components, and a new approach to data compression based on background rejection. The wavelet analysis method described in the paper is applicable to any vector field where the base space is Euclidean (typically R²), that is a mapping from a Euclidean space to a vector bundle. The latter is a collection of vector spaces (called fibres) of equal dimension, attached to each point in the Euclidean base space, and do not need to be related to the base space. The field vectors lie in the fibre space, not the base space, and so can be abstract and of much higher dimension than the base space. This property is very useful for the analysis of multispectral imagery